Trigonometric Identities Question 280
Question: If $ \frac{x}{\cos \theta }=\frac{y}{\cos ( \theta -\frac{2\pi }{3} )}=\frac{z}{\cos ( \theta +\frac{2\pi }{3} )}, $ then $ x+y+z= $
Options:
A) $ 1 $
B) $ 0 $
C) $ -1 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ \frac{x}{\cos \theta }=\frac{y}{\cos ( \theta -\frac{2\pi }{3} )}=\frac{z}{\cos ( \theta +\frac{2\pi }{3} )}=k $
Þ $ x=k\cos \theta $ , $ y=k\cos ( \theta -\frac{2\pi }{3} ) $ , $ z=k\cos ( \theta +\frac{2\pi }{3} ) $
Þ $ x+y+z=k[ \cos \theta +\cos ( \theta -\frac{2\pi }{3} )+\cos ( \theta +\frac{2\pi }{3} ) ] $ $ =k[(0)=0 $
$ \Rightarrow $ $ x+y+z=0 $ .
BETA
